# A study among the Piria Indians of Arizona investigated the relationship between a mother's diabetic status and the number of birth defects in her children. The results appear in the two-way table.

Two-way tables

A study among the Piria Indians of Arizona investigated the relationship between a mother's diabetic status and the number of birth defects in her children. The results appear in the two-way table. $$\text{Diabetic status}\ \begin{array}{ll|c|c|c} && \text { Nondiabetic } & \text { Prediabetic } & \text { Diabetic } \\ \hline & \text { None } & 754 & 362 & 38 \\ \hline & \text { One or more } & 31 & 13 & 9 \end{array}$$

What proportion of the women in this study had a child with one or more birth defects?

$$\begin{array}{ll|c|c|c} && \text { Nondiabetic } & \text { Prediabetic } & \text { Diabetic }&\text{Row total} \\ \hline & \text { None } & 754 & 362 & 38&754+362+38=1154 \\ \hline & \text { One or more } & 31 & 13 & 9&31+13+9=53\\ \hline & \text{Column total}&754+31=785&362+13=375&38+9=47&1154+53=1207 \end{array}$$
We note that the table contains data about 1207 women (as 1207 is mentioned in the bottom right corner of the above table). Next, we note that 53 of the 1207 women had a child with one or more birth defects (as 53 is mentioned in the row "One or more” and in the column "Row Total” of the above table). $$\displaystyle{\frac{{{53}}}{{{1207}}}}\approx{0.0439}$$ Thus a proportion of 0.0439 women had a child with one or more birth defects.